Many people think that all Androids are equal and it's a race to the bottom where the cheapest vendor wins. This could not be farther from the truth. For me, it all began half-a-year ago, when I bought the Samsung Galaxy S III and was absolutely stunned by it, then exploring and comparing it with other Androids. Now that Google has fired a shot across the bow with its low pricing for the unlocked Nexus 4, where does that leave Samsung and its flagship handset?

The N4 is thicker, doesn't have an SD card slot, no removable battery, and has less memory (I have the 32Gb S3).

Yet... I'm still going to sell my S3 because I prefer CM and CM is horrible on the S3.

I love Smart Stay but that is the only feature of the S3 that I care about and I'd be willing to let it go for PhotoSphere, and the fact that I'll likely be able to go to Key Lime Pie (and whatever new apps come with it) the day it comes out.
Who knows... perhaps it'll even have something similar to Smart Stay.

Ok, as an new Android user here's what I don't get: why should I use CM?
I've looked at this at quite some depth but I can't find a single compelling reason. Heck, I can't find a reason to even root my device.
(No, in this case "for the fun of it" does not qualify as compelling)

Ok, as an new Android user here's what I don't get: why should I use CM?

Well, CM generally gets rid of the carrier-applied crap and the crap the manufacturer has added. In case of Samsung's TouchWiz getting rid of that is already enough of a reason to go for CM. Aside from that, well, the answer depends. CM is often faster and more stable than official ROMs and gets security-updates faster.

Heck, I can't find a reason to even root my device.

You obviously don't do anything with it that'd require rooting, then. And if you don't do anything like that then why do you care? It's not like you're expected to root your device even if you have no use for that.

I, personally, use several apps that require rooting, and originally my phone came with Gingerbread -- it was buggy, slow and outdated -- so I rooted my phone and installed a leaked ICS ROM on it to get better battery-life, speed and stability. That's a useful use of the root - capabilities. On the other hand, if I didn't have any apps that require root or didn't need the ability to use custom ROMs then I wouldn't bother rooting, either.

Some apps can provide additional desirable features after you root. Change Hostname if you are frequently on wifi networks (android-jklfadk2qlk3212 sucks as a default hostname). Avast AV can provide better remote control and wipe with root access. Busybox shell environment needs root for full functionality.

There are a number of benefits. One has to decide for themselves if those benefits outweigh the negligable risk.

As for reasons to use CM; if it gets updates more promptly than your vendor-Android distribution fork then it should be a no-brainer. My personal bias towards Nexus devices is specifically because updates come in promptly after Google ships them not when a vendors decides to maybe update there Vendor-Android distro fork.

Granted, I'd drop Android in a heartbeat for a proper general purpose *nix distro.. We'll see how Ubuntu Phone works out though a Debian based firmware i could run against Nexus bare metal ... without a second though.